given the following information, determine which lines, if any, are parallel. state the converse that justifies your answer.
1 answer:
From the information in the diagram found in a similar question online (please see attached drawing), the parallel lines are;
- w||z
- x||y
- x||y
- w||z
- w||z
- x||y
- x||y
- w||z
- x||y
- w||z
Parallel lines are lines that do not meet, when extended indefinitely.
The possible information given as obtained from a similar question posted online are;
1. ‹1 is congruent to ‹5
2. ‹7 is congruent to ‹9
3. m‹8 + m‹9 = 180°
4. ‹16 is congruent to ‹14
5. m‹1 + m‹4 = 180°
6. ‹3 is congruent to ‹13
7. ‹2 is congruent to ‹10
8. ‹11 is congruent to ‹15
9. m‹4 + m‹13 = 180°
10. ‹8 is congruent to ‹6
1. Given that ‹1 is congruent to ‹5 where ‹1 and ‹5 are alternate exterior angles, we have that line <em>w </em>is parallel to line <em>z </em>
- w||z
Theorem (converse); Alternate exterior angles formed by two parallel lines having a common transversal are congruent.
2. ‹7 and ‹9 are alternate interior angles.
Given that ‹7 is congruent to ‹9, therefore;
Line <em>x</em> is parallel to line <em>y</em>
- x||y
Theorem (converse); Alternate interior angles formed by two parallel lines having a common transversal are congruent.
3. Given that m‹8 + m‹9 = 180°, therefore;
‹8 and ‹9 are supplementary angles, formed between lines <em>x </em>and <em>y</em>.
‹8 and ‹9 are also consecutive interior angles.
Theorem (converse); Consecutive interior angles formed between parallel lines are supplementary.
Therefore;
- x||y
4. ‹16 and ‹14 are corresponding angles formed by lines <em>w </em>and <em>z</em>.
Theorem (converse); Corresponding angles formed by parallel lines are congruent.
Given ‹16 congruent to ‹14, we have;
- w||z
5. m‹1 and m‹4 are consecutive exterior angles formed by lines <em>w </em>and <em>z</em>.
Theorem (converse); Consecutive exterior angles formed by two parallel lines are supplementary.
Given that m‹1 + m‹4 = 180°, we have;
- w||z
6. ‹3 and ‹13 are alternate exterior angles formed by lines <em>x </em>and <em>y</em>.
Theorem (converse); Alternate exterior angles formed by parallel lines are congruent.
Given that ‹3 congruent to ‹13, we have;
- x||y
7. ‹2 and ‹10 are corresponding angles formed by lines <em>x </em>and <em>y</em>
Given that ‹2 congruent to ‹10, therefore;
- x||y
8. ‹11 and ‹15 are alternate interior angles formed by lines <em>w </em>and <em>z</em>.
‹11 is congruent to ‹15, therefore;
- w||z
9. ‹4 and ‹13 are consecutive exterior angles formed by lines <em>x </em>and <em>y</em>
m‹4 + m‹13 = 180°, therefore;
- x||y
10. ‹8 and ‹6 are corresponding angles formed by lines <em>w </em>and <em>z</em>.
‹8 is congruent to ‹6, therefore;
- w||z
Learn more about angles formed by parallel lines that have a common transversal here:
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The 1000 cubic centimeters of aluminium is enough for aluminium a trophy that will be in the shape of a right square pyramid and has a base edge of 10 cm and a slant height of 13 cm.
Step-by-step explanation:
The given is,
Volume of aluminium available is 1000 cubic centimeters
Shape of trophy is right square pyramid
Trophy has a base edge of 10 cm and slant height of 13 cm
Step:1
Formula for volume of right square pyramid,
.....................................(1)
Where, a - Base edge value
h - Height of pyramid
From given,
a = 10 cm
h = 13 cm
Equation (1) becomes,
Volume of trophy = 433.33 cubic centimeters
Compare with the volume of available aluminium and volume of right square pyramid,
So, the given volume of aluminium is enough to make right square pyramid shaped trophy.
Result:
The 1000 cubic centimeters of aluminium is enough for aluminium a trophy that will be in the shape of a right square pyramid and has a base edge of 10 cm and a slant height of 13 cm.